Infinite Order Hydrodynamics: An Analytical Example

Abstract

We construct a kinetic model for matter-radiation interactions whose hydrodynamic gradient expansion can be computed analytically up to infinite order in derivatives, in the fully nonlinear regime, and for arbitrary flows. The frequency dependence of the opacity of matter is chosen to mimic the relaxation time of a self-interacting scalar field. In this way, the transient sector simulates that of a realistic quantum field theory. The gradient series is found to diverge for most flows, in agreement with previous findings. We identify, for the model at hand, the mechanism at the origin of the divergence, and we provide a successful regularization scheme. Additionally, we propose a universal qualitative framework for predicting the breakdown of the gradient expansion of an arbitrary microscopic system undergoing a given flow. This framework correctly recovers all previously known instances of gradient expansion divergence. As a new prediction, we show that the gradient expansion diverges when the energy-dependent mean free path is unbounded above.

arXiv comment7 pages (main text) + 2 pages (supplemetary material), 2 captioned figures. Published on PRL (see https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.032302)

References in corpus (42)

• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Derivation of transient relativistic fluid dynamics from the Boltzmann equation
• New theories of relativistic hydrodynamics in the LHC era
• Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation
• First-order relativistic hydrodynamics is stable
• Truncated Moment Formalism for Radiation Hydrodynamics in Numerical Relativity
• Fluid Dynamics far from Local Equilibrium
• Radiative energy loss and v2 spectra for viscous hydrodynamics
• Semi-implicit scheme for treating radiation under M1 closure in general relativistic conservative fluid dynamics codes
• The stickiness of sound: An absolute lower limit on viscosity and the breakdown of second order relativistic hydrodynamics
• Bulk viscosity, particle spectra and flow in heavy-ion collisions
• Anisotropic Hydrodynamics: Three lectures
• Origin of the Relaxation Time in Dissipative Fluid Dynamics
• On the convergence of the gradient expansion in hydrodynamics
• Relativistic anisotropic hydrodynamics
• Relativistic Radiation Magnetohydrodynamics in Dynamical Spacetimes: Numerical Methods and Tests
• Novel Relaxation Time Approximation to the Relativistic Boltzmann Equation
• Relativistic Hydrodynamic Attractors with Broken Symmetries: Non-Conformal and Non-Homogeneous
• Exact hydrodynamic attractor of an ultrarelativistic gas of hard spheres
• Theories of Relativistic Dissipative Fluid Dynamics
• Rigorous bounds on transport from causality
• Causality violations in realistic simulations of heavy-ion collisions
• Bounds on transport from hydrodynamic stability
• Hydrodynamic gradient expansion in linear response theory
• Ab-Initio General-Relativistic Neutrino-Radiation Hydrodynamics Simulations of Long-Lived Neutron Star Merger Remnants to Neutrino Cooling Timescales
• Applying the Gibbs stability criterion to relativistic hydrodynamics
• Thermodynamic equilibrium in relativity: four-temperature, Killing vectors and Lie derivatives
• Modeling general-relativistic plasmas with collisionless moments and dissipative two-fluid magnetohydrodynamics
• Stability and causality of Carter's multifluid theory
• Dispersion relations alone cannot guarantee causality
• Perturbative approaches in relativistic kinetic theory and the emergence of first-order hydrodynamics
• Stress-stress correlator in lambda phi^4 theory: Poles or a Cut?
• Multifluid Modelling of Relativistic Radiation Hydrodynamics
• Relativistic Bulk Rheology: From Neutron Star Mergers to Viscous Cosmology
• Is Relativistic Hydrodynamics always Symmetric-Hyperbolic in the Linear Regime?
• The regime of applicability of Israel-Stewart hydrodynamics
• Relativistic Hydrodynamics: A Singulant Perspective
• Relativistic bulk viscous fluids of Burgers type and their presence in neutron stars
• Hydrodynamic Gradient Expansion Diverges beyond Bjorken Flow
• The unreasonable effectiveness of hydrodynamics in heavy ion collisions
• Far-from-equilibrium kinetic dynamics of $\lambda {\varphi }^4$ theory in an expanding universe
• Relativistic heat conduction in the large-flux regime

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